Quantum simulations with ultracold quantum gases

Nature Physics

Volumn 8, Issue 4, 2012, Pages 267-276

  Bloch, Immanuel ^a,b   Dalibard, Jean ^c   Nascimbène, Sylvain ^a,c  

^a UNIVERSITY OF MUNICH   (Germany)

^b MAX PLANCK INSTITUT FÜR QUANTENOPTIK   (Germany)

^c ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84859337542     PISSN: 17452473     EISSN: 17452481     Source Type: Journal    
DOI: 10.1038/nphys2259     Document Type: Review

References (147)

1. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467-488 (1982).
2. Inguscio, M., Ketterle, W. & Salomon, C. Ultra-cold Fermi Gases: Proceedings of the International School of Physics 'Enrico Fermi', course clxiv, Varenna (2008).
3. Randeria, M., Zwerger, W. & Zwierlein, M. (eds) in The BCS-BEC Crossover and the Unitary Fermi Gas Vol. 836 (Lecture Notes in Physics, Springer, 2012).
4. Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215-1274 (2008).
5. Bardeen, J., Cooper, L. & Schrieffer, J. Theory of superconductivity. Phys. Rev. 108, 1175-1204 (1957).
6. Petrov, D., Salomon, C. & Shlyapnikov, G. Weakly bound dimers of fermionic atoms. Phys. Rev. Lett. 93, 090404 (2004).
7. Werner, F. & Castin, Y. Unitary quantum three-body problem in a harmonic trap. Phys. Rev. Lett. 97, 150401 (2006).
8. Tan, S. Large momentum part of a strongly correlated Fermi gas. Ann. Phys. 323, 2971-2986 (2008).
9. Ho, T. Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett. 92, 090402 (2004).
10. Bertsch, G. in Proceedings of the Tenth International Conference on Recent Progress in Many-Body Theories (eds Bishop, R., Gernoth, K. A., Walet, N. R. & Xian, Y.) (World Scientific, 2000).
11. O'Hara, K., Hemmer, S., Gehm, M., Granade, S. & Thomas, J. Observation of a strongly interacting degenerate Fermi gas of atoms. Science 298, 2179-2182 (2002).
12. Bourdel, T. et al. Experimental study of the BEC-BCS crossover region in lithium 6. Phys. Rev. Lett. 93, 050401 (2004).
13. Stewart, J., Gaebler, J., Regal, C. & Jin, D. Potential energy of a 40K Fermi gas in the BCS-BEC crossover. Phys. Rev. Lett. 97, 220406 (2006).
14. Bartenstein, M. et al. Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas. Phys. Rev. Lett. 92, 120401 (2004).
15. Partridge, G., Li, W., Kamar, R., Liao, Y. & Hulet, R. Pairing and phase separation in a polarized Fermi gas. Science 311, 503-505 (2006).
16. Joseph, J. et al. Measurement of sound velocity in a Fermi gas near a Feshbach resonance. Phys. Rev. Lett. 98, 170401 (2007).
17. Kinast, J. et al. Heat capacity of a strongly interacting Fermi gas. Science 307, 1296-1299 (2005).
18. Navon, N., Nascimbène, S., Chevy, F. & Salomon, C. The equation of state of a low-temperature Fermi gas with tunable interactions. Science 328, 729-732 (2010).
19. Ku, M. J. H., Sommer, A. T., Cheuk, L. W. & Zwierlein, M. W. Revealing the superfluid Lambda transition in the universal thermodynamics of a unitary Fermi gas. Science 335, 563-567 (2012).
20. Carlson, J., Chang, S., Pandharipande, V. & Schmidt, K. Superfluid Fermi gases with large scattering length. Phys. Rev. Lett. 91, 050401 (2003).
21. Astrakharchik, G., Boronat, J., Casulleras, J. & Giorgini, S. Equation of state of a Fermi gas in the BEC-BCS crossover: A quantum Monte Carlo study. Phys. Rev. Lett. 93, 200404 (2004).
22. Altmeyer, A. et al. Precision measurements of collective oscillations in the BEC-BCS crossover. Phys. Rev. Lett. 98, 040401 (2007).
23. Astrakharchik, G. E., Combescot, R., Leyronas, X. & Stringari, S. Equation of state and collective frequencies of a trapped Fermi gas along the BEC-unitarity crossover. Phys. Rev. Lett. 95, 030404 (2005).
24. Nascimbène, S. et al. Fermi-liquid behavior of the normal phase of a strongly interacting gas of cold atoms. Phys. Rev. Lett. 106, 215303 (2011).
25. Sommer, A., Ku, M., Roati, G. & Zwierlein, M. Universal spin transport in a strongly interacting Fermi gas. Nature 472, 201-204 (2011).
26. Zwierlein, M., Schirotzek, A., Schunck, C. & Ketterle, W. Fermionic superfluidity with imbalanced spin populations. Science 311, 492-496 (2006).
27. Shin, Y., Schunck, C., Schirotzek, A. & Ketterle, W. Phase diagram of a two-component Fermi gas with resonant interactions. Nature 451, 689-693 (2008).
28. Shin, Y. Determination of the equation of state of a polarized Fermi gas at unitarity. Phys. Rev. A 77, 041603 (2008).
29. Schirotzek, A., Wu, C., Sommer, A. & Zwierlein, M. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett. 102, 230402 (2009).
30. Nascimbene, S. et al. Collective oscillations of an imbalanced Fermi gas: Axial compression modes and polaron effective mass. Phys. Rev. Lett. 103, 170402 (2009).
31. Haussmann, R. Properties of a Fermi liquid at the superfluid transition in the crossover region between BCS superconductivity and Bose-Einstein condensation. Phys. Rev. B 49, 12975-12983 (1994).
32. Chen, Q., Stajic, J., Tan, S. & Levin, K. BCS-BEC crossover: From high temperature superconductors to ultracold superfluids. Phys. Rep. 412, 1-88 (2005).
33. Burovski, E., Prokof'ev, N., Svistunov, B. & Troyer, M. Critical temperature and thermodynamics of attractive fermions at unitarity. Phys. Rev. Lett. 96, 160402 (2006).
34. Bulgac, A., Drut, J. & Magierski, P. Spin 1/2 fermions in the unitary regime: A superfluid of a new type. Phys. Rev. Lett. 96, 090404 (2006).
35. Hu, H., Liu, X. & Drummond, P. Equation of state of a superfluid Fermi gas in the BCS-BEC crossover. Europhys. Lett. 74, 574-580 (2006).
36. Haussmann, R., Rantner, W., Cerrito, S. & Zwerger, W. Thermodynamics of the BCS-BEC crossover. Phys. Rev. A 75, 023610 (2007).
37. Combescot, R., Alzetto, F. & Leyronas, X. Particle distribution tail and related energy formula. Phys. Rev. A 79, 053640 (2009).
38. Luo, L., Clancy, B., Joseph, J., Kinast, J. & Thomas, J. Measurement of the entropy and critical temperature of a strongly interacting Fermi gas. Phys. Rev. Lett. 98, 080402 (2007).
39. Horikoshi, M., Nakajima, S., Ueda, M. & Mukaiyama, T. Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442-445 (2010).
40. Nascimbène, S., Navon, N., Jiang, K., Chevy, F. & Salomon, C. Exploring the thermodynamics of a universal Fermi gas. Nature 463, 1057-1060 (2010).
41. Van Houcke, K. et al. Feynman diagrams versus Feynman quantum emulator. Preprint at http://arxiv.org/abs/1110.3747 (2011).
42. Rupak, G. Universality in a 2-component Fermi system at finite temperature. Phys. Rev. Lett. 98, 090403 (2007).
43. Liu, X., Hu, H. & Drummond, P. Virial expansion for a strongly correlated Fermi gas. Phys. Rev. Lett. 102, 160401 (2009).
44. Rakshit, D., Daily, K. & Blume, D. Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient. Preprint at http://arxiv.org/abs/1106.5958 (2011).
45. Kohstall, C. et al. Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture. Preprint at http://arxiv.org/abs/ 1112.0020 (2011).
46. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885-964 (2008).
47. Petsas, K., Coates, A. & Grynberg, G. Crystallography of optical lattices. Phys. Rev. A 50, 5173-5189 (1994).
48. Greiner, M., Bloch, I., Mandel, M. O., Hänsch, T. W. & Esslinger, T. Exploring phase coherence in a 2D lattice of Bose-Einstein condensates. Phys. Rev. Lett. 87, 160405 (2001).
49. Sebby-Strabley, J., Anderlini, M., Jessen, P. & Porto, J. Lattice of double wells for manipulating pairs of cold atoms. Phys. Rev. A 73, 033605 (2006).
50. Fölling, S. et al. Direct observation of second-order atom tunnelling. Nature 448, 1029-1032 (2007).
51. Becker, C. et al. Ultracold quantum gases in triangular optical lattices. New J. Phys. 12, 065025 (2010).
52. Tarruell, L., Greif, D., Uehlinger, T., Jotzu, G. & Esslinger, T. Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice. Preprint at http://arxiv.org/abs/1111.5020 (2011).
53. Jo, G-B. et al. Ultracold atoms in a tunable optical kagome lattice. Phys. Rev. Lett. 108, 045305 (2011).
54. Grossmann, F., Dittrich, T., Jung, P. & Hänggi, P. Coherent destruction of tunneling. Phys. Rev. Lett. 67, 516-519 (1991).
55. Eckardt, A., Weiss, C. & Holthaus, M. Superfluid-insulator transition in a periodically driven optical lattice. Phys. Rev. Lett. 95, 260404 (2005).
56. Lignier, H. et al. Dynamical control of matter-wave tunneling in periodic potentials. Phys. Rev. Lett. 99, 220403 (2007).
57. Struck, J. et al. Quantum simulation of frustrated classical magnetism in triangular optical lattices. Science 333, 996-999 (2011).
58. Lee, P., Nagaosa, N. & Wen, X-G. Doping a Mott insulator: Physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17-85 (2006).
59. Jaksch, D. & Zoller, P. The cold atoms Hubbard toolbox. Ann. Phys. 315, 52-79 (2005).
60. Lewenstein, M. et al. Ultracold atomic gases in optical lattices: Mimicking condensed matter physics and beyond. Adv. Phys. 56, 243-379 (2007).
61. Esslinger, T. Fermi-Hubbard physics with atoms in an optical lattice. Annu. Rev. Condens. Mater. Phys. 1, 129-152 (2010).
62. Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546-570 (1989).
63. Jaksch, D., Bruder, C., Cirac, J., Gardiner, C. & Zoller, P. Cold bosonic atoms in optical lattices. Phys. Rev. Lett. 81, 3108-3111 (1998).
64. Greiner, M., Mandel, O., Esslinger, T., Hänsch, T. W. & Bloch, I. Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms. Nature 415, 39-44 (2002).
65. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225-1286 (2010).
66. Mark, M. et al. Precision measurements on a tunable Mott insulator of ultracold atoms. Phys. Rev. Lett. 107, 175301 (2011).
67. Jördens, R., Strohmaier, N., Günter, K., Moritz, H. & Esslinger, T. A Mott Insulator of fermionic Atoms in an optical lattice. Nature 455, 204-207 (2008).
68. Schneider, U. et al. Metallic and insulating phases of repulsively interacting fermions in a 3D optical lattice. Science 322, 1520-1525 (2008).
69. Auerbach, A. Interacting Electrons and Quantum Magnetism (Springer, 1994).
70. Trotzky, S. et al. Time-resolved observation and control of superexchange interactions with ultracold atoms in optical lattices. Science 319, 295-299 (2008).
71. Hazzard, K., Gurarie, V., Hermele, M. & Rey, A. High temperature thermodynamics of fermionic alkaline earth atoms in optical lattices. Preprint at http://arxiv.org/abs/1011.0032 (2010).
72. Gorshkov, A. V. et al. Two-orbital SU(N) magnetism with ultracold alkaline-earth atoms. Nature Phys. 6, 289-295 (2010).
73. Corboz, P., Läuchli, A., Penc, K., Troyer, M. & Mila, F. Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice. Phys. Rev. Lett. 107, 215301 (2011).
74. Hermele, M., Gurarie, V. & Rey, A. Mott insulators of ultracold fermionic alkaline earth atoms: Underconstrained magnetism and chiral spin liquid. Phys. Rev. Lett. 103, 135301 (2009).
75. Pichler, H., Daley, A. & Zoller, P. Nonequilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission. Phys. Rev. A 82, 063605 (2010).
76. Gemelke, N., Zhang, X., Hung, C-L. & Chin, C. In situ observation of incompressible Mott-insulating domains in ultracold atomic gases. Nature 460, 995-998 (2009).
77. Zimmermann, B., Müller, T., Meineke, J., Esslinger, T. & Moritz, H. High-resolution imaging of ultracold fermions in microscopically tailored optical potentials. New J. Phys. 13, 043007 (2011).
78. Nelson, K., Li, X. & Weiss, D. Imaging single atoms in a three-dimensional array. Nature Phys. 3, 556-560 (2007).
79. Bakr, W. S. et al. Probing the superfluid-to-Mott insulator transition at the single-atom level. Science 329, 547-550 (2010).
80. Sherson, J. F. et al. Single-atom-resolved fluorescence imaging of an atomic Mott insulator. Nature 467, 68-72 (2010).
81. Gericke, T., Würtz, P., Reitz, D., Langen, T. & Ott, H. High-resolution scanning electron microscopy of an ultracold quantum gas. Nature Phys. 4, 949-953 (2008).
82. Berg, E., Dalla Torre, E., Giamarchi, T. & Altman, E. Rise and fall of hidden string order of lattice bosons. Phys. Rev. B 77, 245119 (2008).
83. Endres, M. et al. Observation of correlated particle-hole pairs and string order in low-dimensional Mott insulators. Science 334, 200-203 (2011).
84. Saffman, M., Walker, T. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313-2363 (2010).
85. Löw, R. et al. An experimental and theoretical guide to strongly interacting Rydberg gases. Preprint at http://arxiv.org/abs/1202.2871 (2012).
86. Carr, L., DeMille, D., Krems, R. & Ye, J. Cold and ultracold molecules: science, technology and applications. New J. Phys. 11, 055049 (2009).
87. Dalla Torre, E. G., Berg, E. & Altman, E. Hidden Order in 1D Bose Insulators. Phys. Rev. Lett. 97, 260401 (2006).
88. Weitenberg, C. et al. Single-spin addressing in an atomic Mott insulator. Nature 471, 319-324 (2011).
89. Ho, T-L. & Zhou, Q. Universal cooling scheme for quantum simulation. Preprint at http://arxiv.org/abs/0911.5506 (2009).
90. Bernier, J-S. et al. Cooling fermionic atoms in optical lattices by shaping the confinement. Phys. Rev. A 79, 061601(R) (2009).
91. Rabl, P., Daley, A., Fedichev, P., Cirac, J. & Zoller, P. Defect-suppressed atomic crystals in an optical lattice. Phys. Rev. Lett. 91, 110403 (2003).
92. Bakr, W. S. et al. Orbital excitation blockade and algorithmic cooling in quantum gases. Nature 480, 500-503 (2011).
93. Sachdev, S., Sengupta, K. & Girvin, S. Mott insulators in strong electric fields. Phys. Rev. B 66, 075128 (2002).
94. Simon, J. et al. Quantum simulation of antiferromagnetic spin chains in an optical lattice. Nature 472, 307-312 (2011).
95. Ma, R. et al. Photon-assisted tunneling in a biased strongly correlated Bose gas. Phys. Rev. Lett 107, 095301 (2011).
96. Pielawa, S., Kitagawa, T., Berg, E. & Sachdev, S. Correlated phases of bosons in tilted frustrated lattices. Phys. Rev. B 83, 205135 (2011).
97. Cooper, N. R. Rapidly rotating atomic gases. Adv. Phys. 57, 539-616 (2008).
98. Landau, L. D. & Lifshitz, E. M. Quantum Mechanics: Non-Relativistic Theory (Pergamon Press, 1977).
99. Laughlin, R. B. Anomalous quantum Hall effect: An incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395-1398 (1983).
100. Thouless, D. J., Kohmoto, M., Nightingale, M. P. & den Nijs, M. Quantized Hall conductance in a two-dimensional periodic potential. Phys. Rev. Lett. 49, 405-408 (1982).
101. Fetter, A. L. Rotating trapped Bose-Einstein condensates. Rev. Mod. Phys. 81, 647-691 (2009).
102. Schweikhard, V., Coddington, I., Engels, P., Mogendorff, V. P. & Cornell, E. A. Rapidly rotating Bose-Einstein condensates in and near the lowest Landau level. Phys. Rev. Lett. 92, 040404 (2004).
103. Roncaglia, M., Rizzi, M. & Cirac, J. I. Pfaffian state generation by strong three-body dissipation. Phys. Rev. Lett. 104, 096803 (2010).
104. Roncaglia, M., Rizzi, M. & Dalibard, J. From rotating atomic rings to quantum Hall states. Sci. Rep. 1, 1-6 (2011).
105. Berry, M. V. Quantal phase factors accompanying adiabatic changes. Proc. R. Soc. A 392, 45-57 (1984).
106. Dum, R. & Olshanii, M. Gauge structures in atom-laser interaction: Bloch oscillations in a dark lattice. Phys. Rev. Lett. 76, 1788-1791 (1996).
107. Juzeliunas, G. & Öhberg, P. Slow light in degenerate Fermi gases. Phys. Rev. Lett. 93, 033602 (2004).
108. Juzeliunas, G., Ruseckas, J., Öhberg, P. & Fleischhauer, M. Light-induced effective magnetic fields for ultracold atoms in planar geometries. Phys. Rev. A 73, 025602 (2006).
109. Dalibard, J., Gerbier, F., Juzeli Unas, G. & Öhberg, P. Colloquium : Artificial gauge potentials for neutral atoms. Rev. Mod. Phys. 83, 1523-1543 (2011).
110. Lin, Y-J., Compton, R. L., Jiménez-García, K., Porto, J. V. & Spielman, I. B. Synthetic magnetic fields for ultracold neutral atoms. Nature 462, 628-632 (2009).
111. Lin, Y., Jiménez-Garcia, K. & Spielman, I. B. Spin-orbit-coupled Bose-Einstein condensates. Nature 471, 83-86 (2011).
112. Hasan, M. & Kane, C. Colloquium: Topological insulators. Rev. Mod. Phys. 82, 3045-3067 (2010).
113. Qi, X-L. & Zhang, S-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057-1110 (2011).
114. Zhang, C., Tewari, S., Lutchyn, R. M. & Das Sarma, S. px Cipy superfluid from s-wave interactions of fermionic cold atoms. Phys. Rev. Lett. 101, 160401 (2008).
115. Goldman, N. et al. Realistic time-reversal invariant topological insulators with neutral atoms. Phys. Rev. Lett. 105, 255302 (2010).
116. Béri, B. & Cooper, N. R. Z2 topological insulators in ultracold atomic gases. Phys. Rev. Lett. 107, 145301 (2011).
117. Jaksch, D. & Zoller, P. Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms. New J. Phys. 5, 56 (2003).
118. Mueller, E. J. Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids. Phys. Rev. A 70, 041603 (2004).
119. Sørensen, A. S., Demler, E. & Lukin, M. D. Fractional quantum Hall states of atoms in optical lattices. Phys. Rev. Lett. 94, 086803 (2005).
120. Lim, L-K., Smith, C. M. & Hemmerich, A. Staggered-vortex superfluid of ultracold Bosons in an optical lattice. Phys. Rev. Lett. 100, 130402 (2008).
121. Ruostekoski, J., Dunne, G. V. & Javanainen, J. Particle number fractionalization of an atomic Fermi-Dirac gas in an optical lattice. Phys. Rev. Lett. 88, 180401 (2002).
122. Hofstadter, D. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239-2249 (1976).
123. Pannetier, B., Chaussy, J., Rammal, R. & Villegier, J. C. Experimental fine tuning of frustration: Two-dimensional superconducting network in a magnetic field. Phys. Rev. Lett. 53, 1845-1848 (1984).
124. Aidelsburger, M. et al. Experimental realization of strong effective magnetic fields in an optical lattice. Phys. Rev. Lett. 107, 255301 (2011).
125. Cooper, N. R. Optical flux lattices for ultracold atomic gases. Phys. Rev. Lett. 106, 175301 (2011).
126. Cooper, N. R. & Dalibard, J. Optical flux lattices for two-photon dressed states. Europhys. Lett. 95, 66004 (2011).
127. Ruseckas, J., Juzeli Unas, G., Öhberg, P. & Fleischhauer, M. Non-abelian gauge potentials for ultracold atoms with degenerate dark states. Phys. Rev. Lett. 95, 010404 (2005).
128. Osterloh, K., Baig, M., Santos, L., Zoller, P. & Lewenstein, M. Cold atoms in non-abelian gauge potentials: From the Hofstadter 'Moth' to lattice gauge theory. Phys. Rev. Lett. 95, 010403 (2005).
129. Wilczek, F. & Zee, A. Appearance of gauge structure in simple dynamical systems. Phys. Rev. Lett. 52, 2111-2114 (1984).
130. Goldman, N. Quantum Transport in Lattices Subjected to External Gauge Fields (VDM Verlag, 2009).
131. Büchler, H., Hermele, M., Huber, S., Fisher, M. & Zoller, P. Atomic quantum simulator for lattice gauge theories and ring exchange models. Phys. Rev. Lett. 95, 040402 (2005).
132. Sanchez-Palencia, L. & Lewenstein, M. Disordered quantum gases under control. Nature Phys. 6, 87-95 (2010).
133. Billy, J. et al. Direct observation of Anderson localization of matter waves in a controlled disorder. Nature 453, 891-894 (2008).
134. Roati, G. et al. Anderson localization of a non-interacting Bose-Einstein condensate. Nature 453, 895-898 (2008).
135. Kondov, S. S., McGehee, W. R., Zirbel, J. J. & DeMarco, B. Three-dimensional Anderson localization of ultracold matter. Science 334, 66-68 (2011).
136. Castin, Y. & Pricoupenko, L. (eds) The few body problem. C. R. Phys. 12, 1-109 (2011).
137. Trotzky, S. et al. Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas. Nature Phys. 8, 325-330 (2012).
138. Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Colloquium: Nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys. 83, 863-883 (2011).
139. Lamacraft, A. & Moore, J. Potential insights into non-equilibrium behavior from atomic physics. Preprint at http://arXiv.org/abs/1106.3567 1-24 (2011).
140. Pilati, S. & Giorgini, S. Phase separation in a polarized Fermi gas at zero temperature. Phys. Rev. Lett. 100, 030401 (2008).
141. Fuchs, J., Leyronas, X. & Combescot, R. Hydrodynamic modes of a one-dimensional trapped Bose gas. Phys. Rev. A 68, 043610 (2003).
142. Ho, T. & Zhou, Q. Obtaining the phase diagram and thermodynamic quantities of bulk systems from the densities of trapped gases. Nature Phys. 6, 131-134 (2009).
143. Spiegelhalder, F. et al. Collisional stability of 40K immersed in a strongly interacting Fermi gas of 6Li. Phys. Rev. Lett. 103, 223203 (2009).
144. DePue, M. T. M., McCormick, C., Winoto, S. L., Oliver, S. & Weiss, D. D. S. Unity Occupation of Sites in a 3D Optical Lattice. Phys. Rev. Lett. 82, 2262-2265 (1999).
145. Gerbier, F. & Dalibard, J. Gauge fields for ultracold atoms in optical superlattices. New J. Phys. 12, 033007 (2010).
146. Möller, G. & Cooper, N. Condensed ground states of frustrated Bose-Hubbard models. Phys. Rev. A 82, 063625 (2010).
147. Lim, L-K., Hemmerich, A. & Smith, C. M. Artificial staggered magnetic field for ultracold atoms in optical lattices. Phys. Rev. A 81, 023404 (2010).